This invention relates to stepping motors and to the electronic means for energizing them in response to an input, and more specifically to controlling the resonant effect in stepping motors.
This invention is an improvement upon my U.S. Pat. No. 4,100,471 which discloses a stepping motor driver that electronically subdivides the motor's natural step into many small steps. The disclosed electronics consisted of a voltage divider, analog multiplexers to select a voltage divider tap in response to an input, and output amplifiers for energizing the stepping motor in response to the multiplexer outputs. The disclosure explains further that the resistance value of said voltage divider may be adjusted to minimize the effects of resonance.
Patterson, et al in U.S. Pat. No. 4,115,726 analyzes the harmonic behavior of stepping motors. This analysis led them to create sine and cosine current waveforms for their stepping motor and introduce third harmonic sine and cosine currents to minimize the resonance effects. Although the adjustment procedure is a drive with only third harmonic resonance compensation, it rapidly becomes complex as greater compensation is required.
Stepping motors have energy dissipation limits which demand a limit to the maximum current and limit the average current in their windings. Yet stepping motors also are torque limited and demand as much current as possible.
The analysis which Patterson, et al disclosed in U.S. Pat. No. 4,115,726 uses a number of simplifications which have been found to be invalid. The invalid assumptions are: (1) The motor torque is a linear function of current; (2) The frequency of interest is the resonant frequency of the stepping motor; (3) All harmonics are negligable when compared with the fundamental frequency; (4) The motor resonant frequency is not affected by resonance minimization adjustments, and (5) The motor windings of a two-phase motor are 90.degree. apart.
The stepping motor torque is a function of its magnetic flux which is related to winding currents by motor geometry and the familiar non-linear B-H relationship found in magnetic materials. This non-linear relation is an odd function if hysteresis is neglected. Odd functions produce odd harmonics from spectrally pure inputs.
Although Patterson, et al asserts that odd harmonics are the only harmonics necessary to compensate a stepping motor, this added source of odd harmonics was not anticipated.
Large uncompensated harmonics have frustrated attempts to compensate motor resonance. These harmonics create large forces which react with the motor resonance and torque/displacement non-linearities to produce a motion resistant to adjustment.
A reanalysis of the Patterson, et al analysis showed that the frequency of interest needed to be detectable in the motor motion, a task Patterson et al assigned to the motor's mechanical resonance.
The above adjustment problem occurs primarily when making second harmonic adjustments. Although Patterson, et al asserts that the second harmonic is simply a function of phase gain imbalance, further investigation showed that it is also created by interaction of the first and third harmonics since uncompensated third harmonics can contribute significantly to second harmonic resonance or instability and thereby complicate the adjustment process by demanding third harmonic adjustment at the second as well as the fourth harmonic.
The motor torque is a function of winding current, albeit non-linear. The torque variation for various waveforms can be seen in my paper "Analog Operation of Stepping Motors" in the Proceedings of the Sixth Annual Symposium on Incremental Motion Control Systems and Devices, May 1977. Consequently, the resonant frequency, a function of the torque, is a function of winding current. Adjustments in waveshape to avoid resonance, can alter the motor torque which can also alter the resonant frequency. Basically, the torque is changed approximately 20 percent as the waveform changes from a triangle to sine. This will give a 10 percent shift in resonant frequency. Thus the waveshape adjustment appears to be a resonance correction. A separate resonant device which is independent of motor torque avoids this problem.